The performance of many mechanical-structural systems, such as aircraft wings and antenna reflectors, is directly related to the geometric shapes of their components. Such systems would ideally like to adopt different shapes for different operating conditions, but they are generally designed to have one fixed shape that constitutes a compromise with respect to all the operating conditions. Reconfigurable surfaces offer ways to dynamically reconfigure the shape of the material surface under varying operating conditions and external disturbances. This capability will enable systems, such as aircrafts, to maintain enhanced performance and versatility. The most common approach to morph structures is based on compliant mechanisms (see Literature Reference No. 1). A compliant mechanism is a single piece of flexible structure that delivers the desired motion by undergoing elastic deformation as opposed to the rigid body motions in a conventional mechanism. These mechanisms are flexible enough to transmit motions, yet stiff enough to withstand external loads. The hingeless nature of compliant mechanism eliminates the backlash error and effectively reduces the production and maintenance costs associated with systems. Moreover, the distributed compliance throughout the compliant mechanism provides a smooth deformation field, which reduces the stress concentration. Previous research on compliant mechanism synthesis has typically employed a two-step synthesis approach (see Literature Reference No. 2). The two-step approach decomposes the interrelated topology and dimensional syntheses into two separate stages: (1) topology synthesis ensures the motion in the desired output direction and (2) the size and geometry optimization refines the mechanism dimensions to achieve a desired objective such as maximizing displacement. There are successful demonstrations of morphing structures based on the idea of compliant mechanisms (see Literature Reference Nos. 3 through 5).
Most of these efforts are however limited in several ways. First, they are not well suited for large deformation morphing tasks (see Literature Reference No. 6). This is because the amount of elastic energy consumed in morphing with large deformation using these compliant mechanisms is prohibitively large and makes it impractical to implement on real systems. In addition, these mechanisms cannot accomplish significant “Gaussian Curvature” or simultaneous curvature about two orthogonal axes because this requires a change in area in the plane of the deformation. The assumptions made in the design of the morphing strategies based on compliant mechanisms are way too simplified as well. Some of these assumptions include (see Literature Reference No. 5) the requirement that the shape changing object will change from its initial profile to only one target profile and that the compliant mechanism has only a single external input actuator at a specified location. These assumptions are far too restrictive for any general purpose morphing task.
One promising approach for creating large deformation morphing structures is based on using variable stiffness components to provide large deformation without large energy input to the system. Such a system is described in Literature Reference No. 6. A variable stiffness structure consists of constant stiffness material layers and variable modulus material layers arranged in alternating layers. The variable modulus material layers have a material with a changeable elastic modulus in response to an applied energy field so as to allow reversible coupling and decoupling of stress transfer between successive layers of the constant stiffness material layers to provide a change in a bending stiffness of the variable stiffness structure. In a previous invention (see Literature Reference No. 11), distributed genetic algorithms (GA) was applied to design shape morphing strategies for reconfigurable surfaces composed of variable stiffness components. However, Genetic algorithm (GA) is a one shot solution and does not account for the dynamics of the control task. In particular, a one shot solution may possibly violate the strain constraints for morphing structural shapes. Deforming structures composed of variable stiffness components is an ill-posed problem because there can be multiple dynamic control solutions for any given morphing task.
Thus, a continuing need exists for a multi-object control system for variable stiffness structures. The present invention solves this problem by operating on incremental steps which conform to the strain constraints while following the control task's dynamics.